• Quantum Liouville theory provides the simplest example for a two-dimensional conformal field theory with continuous spectrum . It can therefore be regarded as a paradigm for a whole new class of two-dimensional conformal field theories which are neither rational nor quasi-rational. • The quantized Liouville theory is related to quantized spaces of Riemann surfaces. This interpretation should ...

Motivated by the supersymmetric extension of Liouville theory in the recent physics literature, we couple the standard Liouville functional with a spinor field term. The resulting functional is conformally invariant. We study geometric and analytic aspects of the resulting Euler-Lagrange equations, culminating in a blow up analysis.

In this paper, some new estimates on Fej?r sort inequalities via Riemann Liouville fractional integral for the products of two harmonically-convex functions are obtained.